{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CWYWNP3BMLAXF2VNHU25TYDCMV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"922628eb928376e675ebc526cde6d061be952b1bcbc095ec23de379b5ef933b9","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-09T07:57:00Z","title_canon_sha256":"f16e449c8a8ba5d87787d05f644bdee5e2de3050824623aa0f08ca1526ac97e7"},"schema_version":"1.0","source":{"id":"1810.03841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03841","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03841v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03841","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"CWYWNP3BMLAX","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CWYWNP3BMLAXF2VN","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CWYWNP3B","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:4863cf08345523463a50a0b596c139846427fc797798203687f9ae44a633ee93","target":"graph","created_at":"2026-05-18T00:03:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study arithmetic properties of a one-parameter family ${\\mathbf H}$ of H\\'enon maps over the affine line. Given a family of initial points ${\\mathbf P}$ satisfying a natural condition, we show the height function $h_{{\\mathbf P}}$ associated to ${\\mathbf H}$ and ${\\mathbf P}$ is the restriction of the height function associated to a semipositive adelically metrized line bundle on projective line. We then show various local properties of $h_{{\\mathbf P}}$. Next we consider the set $\\Sigma({\\mathbf P})$ consisting of periodic parameter values, and study when $\\Sigma({\\mathbf P})","authors_text":"Liang-Chung Hsia, Shu Kawaguchi","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-09T07:57:00Z","title":"Heights and periodic points for one-parameter families of H\\'enon maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03841","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e20a1e3b3f5621ef804f67969d3ceb5d9532d612867e0a8b80b811adfb8c352","target":"record","created_at":"2026-05-18T00:03:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"922628eb928376e675ebc526cde6d061be952b1bcbc095ec23de379b5ef933b9","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-09T07:57:00Z","title_canon_sha256":"f16e449c8a8ba5d87787d05f644bdee5e2de3050824623aa0f08ca1526ac97e7"},"schema_version":"1.0","source":{"id":"1810.03841","kind":"arxiv","version":1}},"canonical_sha256":"15b166bf6162c172eaad3d35d9e0626576b7162d6a62ed64bf9947dcc03e5ef4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b166bf6162c172eaad3d35d9e0626576b7162d6a62ed64bf9947dcc03e5ef4","first_computed_at":"2026-05-18T00:03:44.413233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:44.413233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+t5zeK/fl3jIHHT90FD3o1Ak/rUv+CY71Cc74pM6FpU1TTWjF4dKdIgjYBNbc1jciWf6UX51rdDjAaE5PxkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:44.413610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e20a1e3b3f5621ef804f67969d3ceb5d9532d612867e0a8b80b811adfb8c352","sha256:4863cf08345523463a50a0b596c139846427fc797798203687f9ae44a633ee93"],"state_sha256":"fd2a4c986f10cb93ddfdfe48ec92fa4fdf1d7f60a748826ccf364b47f960434c"}